Two own goals from Liam Bridcutt and a third by Lewis Dunk helped Liverpool to a 6-1 win over second-tier Brighton at Anfield on Sunday as they set up an FA Cup quarterfinal tie with Stoke.
The Reds, who have not won any silverware since the 2006 FA Cup, face another Championship side in Cardiff in the League Cup final at Wembley next weekend.
But they also moved into the last eight of the FA Cup with a convincing display against Gus Poyet's team.
Martin Skrtel made the breakthrough in the fifth minute and although Kazenga Lua Lua pulled Brighton level, Bridcutt's first own goal sent Liverpool in ahead at the interval.
Andy Carroll scored a third with a low finish just before the hour, Bridcutt and Dunk scored own goals and, after missing a penalty, Luis Suarez added a sixth from close range.
It was the first time in history a team had scored three own goals in one FA Cup tie.
With Suarez, Carroll and Steven Gerrard starting for the first time together, Liverpool wasted little time in going ahead.
Gerrard's corner picked out Skrtel, who peeled away at the near post and glanced a header past Brighton keeper Peter Brezovan.
But the visitors drew level when Lua Lua made Jordan Henderson pay for giving away an unnecessary free-kick on the edge of the area by driving the ball powerfully past Reina at the goalkeeper's near post.
As the hosts continued to offer all of the attacking threat, Carroll headed wide from a Charlie Dam cross, Jose Enrique missed with a right-foot shot after a strong run and Inigo Calderon hacked off the line after Suarez had beaten Brezovan with a stabbed shot.
Charlie Adam drilled over from 25 yards and Carroll also saw a header from a Gerrard cross fly narrowly over the bar.
Lua Lua missed the chance to add a second for Brighton when he saw his effort hit the side-netting after another impressive run.
Brighton were once again grateful for Brezovan, who tipped over from a bending Gerrard free-kick.
But just before the interval the Reds went ahead thanks to Bridcutt's own goal.
Brezovan pushed a corner straight into the air but blocked Suarez's follow-up and when Glen Johnson headed towards the corner, Sam Vokes headed away only for the ball to bounce into the net off Bridcutt.
Liverpool continued to do all of the pressing after the restart, with Suarez's neat chip held by Brezovan.
Henderson failed to worry Brezovan with a long-range effort but Liverpool scored a third just before the hour.
Gerrard slipped a pass wide for Stewart Downing and the winger provided a low cross for Caroll to produce a neat finish at the near post for his sixth goal of the season.
With just under 20 minutes remaining Liverpool scored a fourth when they broke quickly from a Brighton corner and when Gerrard's initial effort was blocked by Brezovan, the Liverpool captain's cross was again turned into his own net by Bridcutt.
Suarez could have made it six after Dirk Kuyt was pulled down by Craig Noone in the area but the Uruguayan's penalty was pushed away by Brezovan.
But with five minutes remaining, Enrique's cross was headed back across goal by Carroll and Suarez nodded in from just a couple of yards out.